ABSTRACT
If two variables are correlated, there are at least three ways we can “explain” the presence of a relationship between them.
It may be that one variable (partly) determines the other, in a sense that has no converse. We say that one is a cause of the other. For example, observing a rat in an activity cage, we say that hunger causes activity. And after a good workout we say activity causes hunger. But we do not say that activity and hunger are merely contingently associated. Both the meaning and the verification of causal claims are deep and controversial matters. It is to be hoped that the reader, like the writer, makes a distinction between “teaching causes learning” and “teaching and learning are activities often found together.”
It may be that the two variables are related effects of a common cause. For example, distinct stock prices vary together from the impact of political events on the psyches of market “players.”
It may be that the two variables are correlated because they measure, or indicate, something in common. This can be literally true. Some tests contain items that can be scored for more than one trait, and the correlation between scores for the traits comes from shared score components. This would generally be regarded as a spurious correlation. But by measuring in common, nothing quite so literal is intended. The notion is that the variables are indicators, “symptoms” or manifestations of the same state of affairs. For example, extraversion is an abstract concept whose instances are the recognized extravert behaviors, and it is therefore circular to say that extraversion “causes” its manifestations. This explanation of relatedness has already been used earlier in a qualitative and intuitive way. At this point we use it to introduce a statistical model to refine our conception of homogeneous tests—of tests whose items are all of the same kind. This is a more general model, and the true-score model is just a special case of it. The model we need deals with relationships between the items, not just relationships between total test scores.
